12/3/24 Sectors, Arcs, Angles, & Tangents

Front

What is a sector in a circle?

Back

A sector is a portion of a circle enclosed by two radii and the arc between them.

Front

How do you calculate the area of a sector?

Back

The area of a sector can be calculated using the formula: \( A = \frac{\theta}{360} \times \pi r^2 \), where \( \theta \) is the central angle in degrees and \( r \) is the radius.

Front

What is the formula for the length of an arc?

Back

The length of an arc can be calculated using the formula: \( L = \frac{\theta}{360} \times 2\pi r \), where \( \theta \) is the central angle in degrees and \( r \) is the radius.

Front

What is a tangent line to a circle?

Back

A tangent line is a straight line that touches the circle at exactly one point and does not cross into the circle.

Front

How do you determine if a line is tangent to a circle?

Back

A line is tangent to a circle if it is perpendicular to the radius drawn to the point of tangency.

Front

What is the relationship between the angles formed by two tangents drawn from a point outside the circle?

Back

The angle formed between two tangents drawn from a point outside the circle is equal to half the difference of the measures of the intercepted arcs.

Front

What is the measure of an angle formed by two tangents to a circle?

Back

The measure of the angle formed by two tangents to a circle is equal to half the difference of the measures of the arcs that the tangents intercept.

Front

How do you find the area of a sector given the radius and angle?

Back

Use the formula: \( A = \frac{\theta}{360} \times \pi r^2 \), substituting the values for \( \theta \) and \( r \).

Front

What is the formula for the area of a circle?

Back

The area of a circle is given by the formula: \( A = \pi r^2 \), where \( r \) is the radius.

Front

What is the difference between a minor arc and a major arc?

Back

A minor arc is the shorter arc connecting two points on a circle, while a major arc is the longer arc connecting the same two points.